Q6 of 26 Page 86

In the figure 6.21, CD is a diameter of the circle with center O. Diameter CD is perpendicular to chord AB at point E. Show that ΔABC is an isosceles triangle.

We know that a perpendicular drawn from the center of a circle on its chord bisects


the chord.


So, AE = EB


In ΔACE and ΔBCE,


AE = EB


∠AEC = ∠BEC = 90°


CE = CE (common)


Δ ACE ≅ Δ BCE (By SAS congruence)


Therefore, AC = BC (by CPCT)


Hence proved that ABC is an isosceles triangle.


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